Why does the equation 35-5x+6x-36=-24-17x+17x+24 have one solution

Combining like terms first

x-1=0

x=1

It has only one solution because only one value of x satisfies the equation.

If it has only one solution that means that there is only one value of x that will fulfill this equation

35 - 5x + 6x - 36 = - 24 - 17x + 17x + 24

-5x + 6x - 36 = - 24 - 17x + 17x + 24 - 35

x - 36 = - 24 + 24 - 35 (I just canceled out the 17x because it would have justy made the process longer if I moved them over)

x = - 24 + 24 - 35 + 36

x = - 35 + 36

x = 1